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Anomalies in Tournament Design: the Madness of March Madness

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Anomalies in Tournament Design: the Madness of March Madness Working Paper Series, Paper No. 09-10 Anomalies in Tournament Design: The Madness of March Madness Robert Baumann†, Victor A. Matheson††, and Cara Howe††† October 2009 Abstract Tournament design is of crucial importance in competitive sports. The primary goal of effective tournament design is to provide incentives for the participants to maximize their performance both during the tournament and in the time period leading up to the tournament. In spectator sports, a secondary goal of tournament design is to also promote interesting match ups that generate fan interest. Seeded tournaments, in general, promote both goals. Teams or individuals with strong performances leading up to a tournament receive higher seeds which increase their chances of progressing further in the tournament. Furthermore, seeding ensures that the strongest teams or players are most likely to meet in the final rounds of the tournament when fan interest is at its peak. Under some distributions of team or player skill, however, a seeding system can introduce anomalies that could affect incentives. Our analysis of the NCAA men’s basketball tournament uncovers such an anomaly. The seeding system in this tournament gives teams with better success in the regular season more favorable first round match ups, but the tournament is not reseeded as the games progress. Therefore, while higher seeds progress to the 2nd round of the tournament at uniformly higher rates than lower seeds, this relationship breaks down in later rounds. We find that 10th and 11th seeds average more wins and typically progress farther in the tournament than 8th and 9th seeds. This finding violates the intended incentive structure of seeded tournaments. JEL Classification Codes: L83, D02 Keywords: basketball, tournament design, sports, NCAA †Robert Baumann, Department of Economics, Box 192A, College of the Holy Cross, Worcester, MA 01610-2395, 508-793-3879 (phone), 508-793-3708 (fax), [email protected] ††Victor A. Matheson, Department of Economics, Box 157A, College of the Holy Cross, Worcester, MA 01610-2395, 508-793-2649 (phone), 508-793-3708 (fax), [email protected] †††Cara Howe, Department of Economics, College of the Holy Cross, Worcester, MA 01610-2395, [email protected] Introduction Tournament design is an integral part of the operation of any sports league or event, and contest design has been examined by numerous economists. Szymanski (2003) provides a comprehensive overview but notes that “issues deserving further attention include the value of screening [and] the role of handicapping.” This paper examines these issues by focusing on the structure of the National Collegiate Athletic Association’s (NCAA) men’s basketball tournament, also known as “March Madness.” A primary goal of effective tournament design is to provide incentives for the participants to maximize their performance both during the tournament and in the time period leading up to the tournament. In spectator sports, a second goal of tournament design is to promote interesting match ups that generate fan interest. Of course, a huge variety of contest designs can be utilized both in individual and team sports. One broad type of tournament design is of the “round robin” tournament, or some variant, in which every participant plays games against each of the other contestants. Most regular season games in sports leagues utilize a variation of the round robin tournament. In a round robin tournament, teams or individuals play a number of matches against different opponents with the winner of the most games being declared the victor. For example, in the overwhelming majority of European soccer leagues each team plays one game at home and one game on the road against each of the other teams in the league. In a 20-team league like the English Premier League or Spain’s La Liga, this results in a 38 game schedule for each team with the most successful team being named the annual league champion. 2 The majority of American professional sports leagues utilize unbalanced round robin tournaments for their regular season contests where teams play many or all of the other teams in the league but play more games against geographical or historical rivals. In the National Football League, for example, each team plays a home and away series with each team in its own division and then games against 10 of the remaining 28 teams in the league. In the National Basketball Association, each team plays two home and away series with every team in their own division, either 3 or 4 games against every remaining team in their conference, and a single home and away series with each team in the opposite conference. In most American professional sports leagues, the top teams then qualify for a post-season playoff tournament The other major category of tournament is the “elimination tournament” where contestants match up against one another and the winners progress while the losers are eliminated from further participation in the tournament. As with round robin tournaments, numerous variations on this the concept exist. In a standard single elimination tournament, a single game determines which player or team will advance. Both the NFL’s post-season playoff system as well as the National Collegiate Athletic Association’s (NCCA) men’s and women’s basketball tournaments are set up as single elimination tournaments. Most tennis tournaments and match-play golf tournaments are also examples of simple single elimination tournaments. Another common variant on the elimination tournament uses series of games between two opponents to determine who advances in the tournament. For example, in the NBA the winner of a best of seven series goes through to the next round, while in some stages of the European Champions League in soccer as well as many levels of the World Cup qualifying tournaments, the winner of 3 a home and away series advances. A third variant is the “double elimination” tournament where a team is removed from the tournament once it has lost two contests. Finally, many sports utilize a combination of round robin and single elimination tournament. For example, as noted previously, American sports leagues typically use a round robin format during the regular season and then progress to an elimination tournament for playoffs. The FIFA World Cup uses four-team round robin tournaments in the first round of the competition before progressing to a 16-team single game elimination format. Screening, Seeding, and Handicapping Regardless of the type of tournament design used, a variety of methods can be used to determine which teams or players will play one another. Screening refers to which teams or players will be eligible for a competition. Seeding and handicapping refers to placement of teams that have been selected for a tournament. Of course, tournaments themselves are frequently used for screening purposes for future tournaments. Regular season results are used as screening for playoffs in American leagues or for advancement into European-wide tournaments such as the UEFA or Champions League tournaments in European soccer. Confederation results are used for screening advancement into the World Cup. In leagues with promotion and relegation, a prior season’s record serves as a screening device for which league a team will play in during the current season. Similarly, in the Professional Golfers Association (PGA), players with a certain level of winnings during the previous season are eligible to compete in professional tournaments during the current season. 4 Once screening has been achieved, in a full round robin tournament, all teams play an identical schedule, so seeding or handicapping the teams in the tournament is unnecessary. In other tournament designs, however, decisions must be made about how match ups will be set. In some cases, competition choices will be made without specific consideration of the skill of the teams or players involved. For example, in leagues such as the NBA and MLB, where an unbalanced schedule is played, the implementation of the schedule does not generally depend on the prior success of the teams involved but instead depends largely on geography and historical accident. Similarly, some elimination tournaments use a random draw where match ups are done by chance without consideration of the skill of the teams or players involved. The initial groups for round robin play in the World Cup are chosen at least in part by chance during the highly anticipated World Cup draw. While teams are placed in various equivalence classes based on performance, within each class, teams are chosen at random. Given the existence of variation in skills within each class, pure luck can result in some four-team groups ending up with stronger teams on average than other groups. Every country dreads being randomly placed in the so-called “Group of Death” with the strongest teams on average. Conversely, tournaments can be designed with team or player strength in mind. In the NFL, the league uses a weighted schedule to promote competitive balance. All teams play a full round robin schedule with the other 3 teams in their division, and divisions are created based upon geography and historical rivalry, but the remaining 10 games of the season are scheduled based upon the previous season’s standings with stronger teams 5 being scheduled against better opponents. In the case of the NFL, strong teams are “rewarded” for their success by playing a harder schedule in the following season. More commonly, good teams or players are rewarded for their success through seeding. In both round robin and elimination tournaments, prior success can be accounted for by the use of seeding, where top seeded players are assigned to play lower quality teams or players in early rounds. Playoffs in American professional leagues are typically fully seeded tournaments where the team with the best record in the regular season plays in the first round the team with the worst record in the regular season that qualified for the playoffs.
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